On the Effect of Correlations on Rank Histograms: Reliability of Temperature and Wind-speed Forecasts from Fine-scale Ensemble Reforecasts

The rank histogram (RH) is a visual tool for assessing the reliability of ensemble forecasts, i.e., the degree to which the forecasts and the observations have the same distribution. But it is already known that in certain situations it conveys misleading information. Here, it is shown that a temporal correlation can lead to a misleading RH, but such a correlation contributes only to the sampling variability of the RH, and so it is accounted for by producing a RH which explicitly displays sampling variability. A simulation is employed to show that the variance within each ensemble member (i.e., climatological variance), the correlation between ensemble members, and the correlation between the observations and the forecasts, all have a confounding effect on the RH, making it difficult to use the RH for assessing the climatological component of forecast reliability. It is proposed that a “Residual” Q-Q plot (denoted R-Q-Q plot) is better suited than the RH for assessing the climatological component of forecast reliability. Then, the RH and R-Q-Q plots for temperature and wind-speed forecasts at 90 stations across the continental US are computed. A wide range of forecast reliability is noted. For some stations, the non-reliability of the forecasts can be attributed to bias and/or under- or over- climatological dispersion. For others, the difference between the distributions can be traced to lighter or heavier tails in the distributions, while for other stations the distributions of the forecasts and the observations appear to be completely different. A spatial signature is also noted and discussed briefly.